Memorizing Clues but Not the Code

Algebra Level 2

I got locked out of my work building, but I forgot the code. However, I managed to remember some way more complicated clues. Can you write the code down [e.g. let's say the code is 1,2,3,4. You would write your answer as 1234].

Clues: The fifth number plus the third number equals fourteen. The fourth number is one more than the second number. The first number is one less than twice the second number. The second number plus the third number equals ten. The third number is one less that the first number. The sum of all five numbers is 30.

What were the five numbers and in what order?

The answer is 74658.

1 solution

Naitik Sanghavi
May 10, 2015

Let the 1st digit be "a"

              2nd digit be "b"

             3rd digit be "c"

              4th digit be "d"

               5th digit be "e".(All five in order)

From the given clues,We have

e+c=14........eq.1

d-1=b.........eq.2

a=2b-1.......eq.3

b+c=10.......eq.4

c+1=a.........eq.5

a+b+c+d+e=30........eq.6

Now subtracting eq.4 from eq.2,

We have,

c+d=11

Now again subtracting eq.5 from eq.4,

We have,

a+b=11

Therefore,

a+b=c+d

Now subtracting eq.5 from eq.1,

We have ,

a+e=15

Now substituting value of a+e and c+d in eq.6,

We get,

b=4.

Therfore,

a=7

b=4

c=6

d=5

e=8,

So,the required code in order is ,74658.

This is my first solution,so don't mind if there r some mistakes.

Thanks,hope everyone will understand this.

Memorizing Clues but Not the Code

The answer is 74658.

1 solution

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